Basic properties
| Modulus: | \(8712\) | |
| Conductor: | \(8712\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8712.ek
\(\chi_{8712}(5,\cdot)\) \(\chi_{8712}(317,\cdot)\) \(\chi_{8712}(389,\cdot)\) \(\chi_{8712}(509,\cdot)\) \(\chi_{8712}(533,\cdot)\) \(\chi_{8712}(581,\cdot)\) \(\chi_{8712}(653,\cdot)\) \(\chi_{8712}(797,\cdot)\) \(\chi_{8712}(1037,\cdot)\) \(\chi_{8712}(1109,\cdot)\) \(\chi_{8712}(1181,\cdot)\) \(\chi_{8712}(1301,\cdot)\) \(\chi_{8712}(1325,\cdot)\) \(\chi_{8712}(1373,\cdot)\) \(\chi_{8712}(1445,\cdot)\) \(\chi_{8712}(1589,\cdot)\) \(\chi_{8712}(1829,\cdot)\) \(\chi_{8712}(1901,\cdot)\) \(\chi_{8712}(1973,\cdot)\) \(\chi_{8712}(2093,\cdot)\) \(\chi_{8712}(2117,\cdot)\) \(\chi_{8712}(2165,\cdot)\) \(\chi_{8712}(2237,\cdot)\) \(\chi_{8712}(2381,\cdot)\) \(\chi_{8712}(2621,\cdot)\) \(\chi_{8712}(2693,\cdot)\) \(\chi_{8712}(2765,\cdot)\) \(\chi_{8712}(2885,\cdot)\) \(\chi_{8712}(2909,\cdot)\) \(\chi_{8712}(2957,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((6535,4357,1937,5689)\) → \((1,-1,e\left(\frac{5}{6}\right),e\left(\frac{37}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8712 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{74}{165}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{148}{165}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{27}{55}\right)\) |